Abstract: In-situ observation, remote sensing, analytic and numerical models are all important tools in physical oceanography research. In this dissertation, all of these tools, combined with upwelling indices, are used to explore coastal upwelling responses to wind stress, wind duration, shelf slope, tide, cape, and coastal canyon. First, two upwelling indices (UI) derived from remotely sensed data, which are related to offshore Ekman transport (UIW) and the sea surface temperature (SST; UISST), are evaluated to study the spatial and temporal variation of the Benguela Upwelling System (BUS). The comparison presents the advantages and disadvantages of using UISST and UIW to measure upwelling intensity, when chlorophyll-a (Chl-a) concentration is used as a proxy for upwelling enhanced relative biomass. The causes for the discrepancies of temporal and spatial variations of UISST, UIW and Chl-a in the BUS area are discussed. By examining the UISST, UIW and Absolute Dynamic Topography (ADT) at 27-28oS, it is found that the extension of the upwelling band is largely impacted by the anti-cyclonic eddy there. Furthermore, this dissertation discusses the Benguela Niños in 2006, and estimates the contribution from the wind to the total upwelling intensity off Hondeklip and Cape Columbine based on these remote sensing data. Second, to understand the differences in upwelling tendency between the east and west coasts of the U.S., idealized analytical and numerical model experiments were performed to examine upwelling responses to wind and shelf slope. The primary results show that steeper slope leads to narrower cross-shore width of surface Ekman divergence (WSED) and larger vertical velocity, while stronger upwelling favorable wind stress induces a broader WSED and larger vertical velocity. Meanwhile, wind duration is substantial to determine both the area and intensity of upwelling off a coast. The tendencies for cold upwelling areas off both coasts are compared by the upwelling age, which is defined as the ratio of the duration of upwelling favorable wind to the advection time. The advection time, defined as the time scale for cold water to be advected from the pycnocline to the ocean surface, is improved to comprise of climbing time and upwelling time. The latter is related to the upwelling divergence driven by surface Ekman flow. The depth of the "turning point" of these two processes is approximately 0.9DE where DE is the Ekman depth. The new formula for the advection time is found to be consistent with estimates derived from the use of particle trajectory analysis in the numerical model. The consideration of upwelling age shows that differences in wind forcing are more important than bottom slope when accounting for different characteristics of upwelling areas off the California and New Jersey coasts. Third, satellite images of SST show that the location of cross-shore SST minimum (LCSM) stretches along the isobaths in the Northwest Africa Upwelling System. To understand and interpret these observations better, a two-dimensional analytical model is set up, which takes into account the surface and bottom Ekman transports and the alongshore geostrophic current, as well as bottom friction and variation in bottom topography. The structure of vertical velocity with a realistic topography clearly illustrates the variation of SST drop in a sample cross-shore section. Some idealized theoretical model experiments are carried out to examine the effects of eddy viscosity, Coriolis force, and cross-shore wind on the location of the cross-shore maximum upwelling intensity. The results show that the cross-shore wind largely impacts on the location where the coldest water outcrops through an adjustment of the cross-shore pressure gradient. This is also verified by the remotely sensed data, which indicate that the maximum correlation coefficient between cross-shore wind stress and the depth of LCSM is -0.65 with a lag of approximately 1 day. Finally, a combination of observations and numerical model is used to reveal the upwelling features and mechanisms in the northern Taiwan Strait during summer. The remote sensing data show a strip of upwelling in the region, which occurs more than half a summer. The upwelling probability map indicates there are two upwelling cores, one located downstream of Pingtan Island formed by cape effect and the other over the coastal canyon off the Sansha Bay. Remote sensing data and numerical model results suggest that the southerly wind plays a key role in shaping this upwelling strip, while the tide-enhanced vertical eddy viscosity results in an offshore shift of the strip. Further numerical experiments using idealized cape and coastal canyon topography show that vertical velocity is intensified downstream of the cape and canyon. The balance of vorticity equation shows that relative vorticity change along a streamline and frictional diffusion of vorticity are responsible for the vertical velocity off the cape and within and around the canyon. The relative vorticity change along a streamline produces positive vertical velocity downstream of the cape and canyon, and becomes the dominant upwelling mechanism there. In summary, this dissertation gives an insight into the advantages and disadvantages of using UIW and UISST as upwelling indices. As an improvement of UIW, upwelling age theory is explored to include climbing and upwelling processes, which considers the effects of wind duration, wind stress and shelf slope. Furthermore, how the dynamical factors shift the cross-shore maximum upwelling intensity, and why the upwelling is intensified downstream of cape and coastal canyon are studied, which throw light on the coastal upwelling research.